Add zk-discrete-log-Proof example over secp256k1 using noir_bigcurve

[cypriansakwa]

Description

Problem

Resolves #89

Summary

This PR adds a new example to the repository: a zero-knowledge discrete logarithm proof circuit over the secp256k1 elliptic curve, using the noir_bigcurve library. The circuit demonstrates how to prove knowledge of a secret scalar ( k ) such that ( Q = k \cdot G ), where ( G ) and ( Q ) are public points on secp256k1, without revealing ( k ). This is a foundational primitive for privacy-preserving authentication and cryptographic protocols.

The example includes:

• A Noir circuit that:
  • Accepts ( G ), ( Q ) as public inputs and ( k ) as a private (witness) input.
  • Verifies that ( Q = k \cdot G ) on secp256k1, leveraging noir_bigcurve.
• Unit tests covering:
  • Correct proof for valid ( k, G, Q ) tuples
  • Rejection of incorrect proofs (wrong ( Q ), not-on-curve points)
• A README.md explaining:
  • The cryptographic context and purpose
  • How to run the example and tests

Additional Context

• This example serves as an educational resource for developers interested in building zero-knowledge proofs over real-world elliptic curves (such as those used in Bitcoin/Ethereum).
• It demonstrates Noir's capabilities for high-level, safe, and expressive zk-circuit development.
• Feedback and suggestions are welcome for further improvement or additional tests.

PR Checklist

• I have tested the changes locally.
• I have formatted the changes with Prettier and/or cargo fmt on default settings.